Details

Time bar (total: 4.0m)

sample69.0ms

Algorithm
intervals
Results
27.0ms68×body640valid
13.0ms133×body80valid
8.0ms17×body1280valid
6.0ms20×body320valid
4.0ms18×body160valid

simplify116.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
116.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize37.0ms

Local error

Found 4 expressions with local error:

2.2b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
743×*-un-lft-identity
715×times-frac
544×add-sqr-sqrt
494×add-cube-cbrt
468×prod-diff
236×associate-+l+
99×distribute-lft-out
72×div-inv
58×associate-/r/
29×flip3-+ flip-+
22×distribute-lft-out--
20×difference-of-squares
18×fma-neg
13×fma-def
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u difference-of-sqr-1 div-exp insert-posit16 log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp clear-num sum-log sub-neg frac-2neg diff-log 1-exp frac-sub pow-flip inv-pow
1×+-commutative associate-+l-
Counts
4 → 648
Calls
4 calls:
Slowest
285.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
38.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
17.0ms
(/ 1 (- x 1))
16.0ms
(/ 1 (+ x 1))

series186.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
42.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
17.0ms
(/ 1 (+ x 1))
14.0ms
(/ 1 (- x 1))

simplify2.2m

Counts
879 → 660
Calls
879 calls:
Slowest
592.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
577.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))))
560.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
550.0ms
(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
547.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ 1 (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

60.8b
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
2.2b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
329×times-frac
254×add-sqr-sqrt
237×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
38×div-inv
26×associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×cbrt-prod sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 322
Calls
4 calls:
Slowest
163.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
0.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))

series1.2s

Counts
4 → 8
Calls
4 calls:
Slowest
880.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
316.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify40.6s

Counts
287 → 330
Calls
287 calls:
Slowest
602.0ms
(fma (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ 1 (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
534.0ms
(+ (* (- (* 1 x) (* (+ x 1) 2)) (+ (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (* (+ x 1) x) (+ (pow (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
525.0ms
(fma (/ 1 1) (/ 1 (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
438.0ms
(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (+ (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))))
395.0ms
(+ (* (- (pow (/ 1 (+ x 1)) 3) (pow (/ 2 x) 3)) (- (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))) (* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- (* (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))))

prune3.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

60.8b
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
60.8b
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
2.2b
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))
1.0b
(cbrt 2)

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
368×*-un-lft-identity
329×times-frac
253×add-sqr-sqrt
236×associate-+l+ add-cube-cbrt
234×prod-diff
67×distribute-lft-out
39×div-inv
26×associate-/r/
25×add-log-exp
17×flip3-+ flip-+
13×fma-def
12×sum-log distribute-lft-out--
6×frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-prod diff-log
2×flip3-- frac-sub fma-udef flip--
1×+-commutative associate-+r+ sub-neg pow1/3 associate-+l-
Counts
4 → 324
Calls
4 calls:
Slowest
219.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))
1.0ms
(cbrt 2)
0.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
0.0ms
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))

series2.1s

Counts
4 → 10
Calls
4 calls:
Slowest
981.0ms
(fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))
839.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
320.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))
0.0ms
(cbrt 2)

simplify38.9s

Counts
291 → 334
Calls
291 calls:
Slowest
550.0ms
(+ (* (- (* (/ 1 (+ 1 x)) (/ 1 (+ 1 x))) (* (/ 2 x) (/ 2 x))) (- (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))) (* (+ (/ 1 (+ 1 x)) (/ 2 x)) (- (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (* (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))))
487.0ms
(* (+ (/ 1 (+ 1 x)) (/ 2 x)) (+ (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (* (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))) (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))))
483.0ms
(fma (/ (sqrt 1) (sqrt (+ 1 x))) (/ (sqrt 1) (sqrt (+ 1 x))) (- (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))))
481.0ms
(* (* (+ 1 x) x) (+ (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (- (* (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))) (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))))
400.0ms
(+ (* (- (* 1 x) (* (+ 1 x) 2)) (- (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))) (* (* (+ 1 x) x) (- (* (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))) (fma (- (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))) (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x)))))) (* (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))) (+ (fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))))

prune4.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize205.0ms

Local error

Found 4 expressions with local error:

29.5b
(fma (- x (fma x 2 2)) (fma (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (/ 1 (- x 1)) (- (/ 1 (- x 1)) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (* (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (fma x x x)))
21.9b
(* (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (fma x x x))
15.6b
(* (fma (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x)))) (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x)))) (* (- (/ 1 (- x 1)) (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))))) (/ 1 (- x 1)))) (fma x x x))
1.0b
(cbrt 2)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
5×fma-udef
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×pow1/3
Counts
4 → 71
Calls
4 calls:
Slowest
6.0ms
(* (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (fma x x x))
5.0ms
(* (fma (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x)))) (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x)))) (* (- (/ 1 (- x 1)) (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))))) (/ 1 (- x 1)))) (fma x x x))
1.0ms
(cbrt 2)
0.0ms
(fma (- x (fma x 2 2)) (fma (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (/ 1 (- x 1)) (- (/ 1 (- x 1)) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (* (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (fma x x x)))

series424.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
246.0ms
(fma (- x (fma x 2 2)) (fma (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (/ 1 (- x 1)) (- (/ 1 (- x 1)) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (* (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (fma x x x)))
99.0ms
(* (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))) (fma x x x))
79.0ms
(* (fma (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x)))) (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x)))) (* (- (/ 1 (- x 1)) (- (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))) (* (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))) (/ (cbrt 2) (cbrt x))))) (/ 1 (- x 1)))) (fma x x x))
0.0ms
(cbrt 2)

simplify4.4s

Counts
37 → 81
Calls
37 calls:
Slowest
289.0ms
(+ (* 9 (/ 1 (pow x 3))) (+ (* 4 (/ 1 (pow x 2))) (/ 1 x)))
284.0ms
(+ (* 9 (/ 1 (pow x 3))) (+ (* 4 (/ 1 (pow x 2))) (/ 1 x)))
213.0ms
(sqrt (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))))))))
211.0ms
(* (sqrt (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))))))) (sqrt (fma x x x)))
206.0ms
(* (sqrt (fma (/ (/ 1 (- x 1)) (- x 1)) (/ 1 (- x 1)) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (* (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))) (- (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x)))) (* (/ (cbrt 2) (cbrt x)) (* (/ (cbrt 2) (cbrt x)) (/ (cbrt 2) (cbrt x))))))))) (sqrt (fma x x x)))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 21.7b

bsearch182.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
844.0ms1885×body640valid
283.0ms4153×body80valid
236.0ms584×body1280valid
184.0ms912×body320valid
58.0ms469×body160valid