Details

Time bar (total: 38.8s)

sample30.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify23.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
23.0ms
(/ x (+ (* x x) 1))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 1 expressions with local error:

15.1b
(/ x (fma x x 1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
8.0ms
(/ x (fma x x 1))

series79.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
79.0ms
(/ x (fma x x 1))

simplify1.2s

Counts
28 → 33
Calls
28 calls:
Slowest
244.0ms
(- (+ x (pow x 5)) (pow x 3))
198.0ms
(/ (* (* x x) x) (* (* (fma x x 1) (fma x x 1)) (fma x x 1)))
191.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
163.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
46.0ms
(/ (* (cbrt x) (cbrt x)) (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))

prune296.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

15.0b
(sqrt (fma x x 1))
15.0b
(sqrt (fma x x 1))
0.0b
(/ x (sqrt (fma x x 1)))
0.0b
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 252
Calls
4 calls:
Slowest
9.0ms
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
4.0ms
(/ x (sqrt (fma x x 1)))
1.0ms
(sqrt (fma x x 1))
1.0ms
(sqrt (fma x x 1))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(/ x (sqrt (fma x x 1)))
89.0ms
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
71.0ms
(sqrt (fma x x 1))
49.0ms
(sqrt (fma x x 1))

simplify15.7s

Counts
362 → 264
Calls
362 calls:
Slowest
436.0ms
(/ (/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
393.0ms
(/ (* (* (/ x (sqrt (fma x x 1))) (/ x (sqrt (fma x x 1)))) (/ x (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
392.0ms
(/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
311.0ms
(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))
284.0ms
(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))

prune2.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

15.0b
(sqrt (fma x x 1))
15.0b
(sqrt (fma x x 1))
0.5b
(log1p (/ x (sqrt (fma x x 1))))
0.0b
(/ x (sqrt (fma x x 1)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv log1p-udef clear-num frac-2neg div-exp log1p-expm1 div-inv
Counts
4 → 86
Calls
4 calls:
Slowest
5.0ms
(/ x (sqrt (fma x x 1)))
1.0ms
(sqrt (fma x x 1))
1.0ms
(sqrt (fma x x 1))
0.0ms
(log1p (/ x (sqrt (fma x x 1))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(log1p (/ x (sqrt (fma x x 1))))
103.0ms
(/ x (sqrt (fma x x 1)))
50.0ms
(sqrt (fma x x 1))
48.0ms
(sqrt (fma x x 1))

simplify4.0s

Counts
69 → 98
Calls
69 calls:
Slowest
373.0ms
(- (+ (* 2 (log (/ -1 x))) (+ (log 1/2) (* 11/32 (/ 1 (pow x 4))))) (* 3/4 (/ 1 (pow x 2))))
319.0ms
(/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
293.0ms
(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))
282.0ms
(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))
240.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune916.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

15.4b
(cbrt (fma x x 1))
15.4b
(cbrt (fma x x 1))
15.4b
(cbrt (fma x x 1))
6.2b
(* (/ 1 (* (cbrt (fma x x 1)) (cbrt (fma x x 1)))) (/ x (cbrt (fma x x 1))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
43×add-sqr-sqrt
33×times-frac
25×*-un-lft-identity
22×associate-*r* add-cube-cbrt
21×cbrt-prod
20×prod-exp
18×add-cbrt-cube
15×div-exp
9×unswap-sqr
8×cbrt-unprod
7×cbrt-undiv associate-*l*
6×pow1
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×div-inv
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 115
Calls
4 calls:
Slowest
76.0ms
(* (/ 1 (* (cbrt (fma x x 1)) (cbrt (fma x x 1)))) (/ x (cbrt (fma x x 1))))
2.0ms
(cbrt (fma x x 1))
2.0ms
(cbrt (fma x x 1))
1.0ms
(cbrt (fma x x 1))

series542.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(cbrt (fma x x 1))
143.0ms
(cbrt (fma x x 1))
143.0ms
(cbrt (fma x x 1))
75.0ms
(* (/ 1 (* (cbrt (fma x x 1)) (cbrt (fma x x 1)))) (/ x (cbrt (fma x x 1))))

simplify11.0s

Counts
91 → 127
Calls
91 calls:
Slowest
996.0ms
(* (/ (* (* 1 1) 1) (* (fma x x 1) (fma x x 1))) (* (* (/ x (cbrt (fma x x 1))) (/ x (cbrt (fma x x 1)))) (/ x (cbrt (fma x x 1)))))
720.0ms
(* (* (* (/ 1 (* (cbrt (fma x x 1)) (cbrt (fma x x 1)))) (/ 1 (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))) (/ 1 (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))) (/ (* (* x x) x) (fma x x 1)))
518.0ms
(* (/ (* (* 1 1) 1) (* (fma x x 1) (fma x x 1))) (/ (* (* x x) x) (fma x x 1)))
298.0ms
(- (+ (pow (/ -1 x) -2/3) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))) (* 1/9 (pow (/ 1 (pow x 10)) 1/3)))
294.0ms
(- (+ (pow (/ 1 x) -2/3) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))) (* 1/9 (pow (/ 1 (pow x 10)) 1/3)))

prune974.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch79.0ms

end0.0ms

sample600.0ms

Algorithm
intervals
Results
493.0ms8000×body80valid