Details

Time bar (total: 1.1m)

sample146.0ms

Algorithm
intervals
Results
118.0ms710×body80valid

simplify151.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
151.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1)

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b
(fma (* a a) a (* a a))
0.0b
(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0b
(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 44
Calls
4 calls:
Slowest
1.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms
(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0ms
(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))
0.0ms
(fma (* a a) a (* a a))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
117.0ms
(fma (* a a) a (* a a))
96.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
74.0ms
(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.6s

Counts
12 → 56
Calls
12 calls:
Slowest
413.0ms
(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
350.0ms
(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
344.0ms
(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
325.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
288.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune845.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
15.0ms
(* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
340.0ms
(* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
297.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
286.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
272.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

simplify13.5s

Counts
65 → 97
Calls
65 calls:
Slowest
918.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
479.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
459.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
447.0ms
(* (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
424.0ms
(* (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 59
Calls
4 calls:
Slowest
2.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
292.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
264.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
252.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

simplify6.2s

Counts
27 → 71
Calls
27 calls:
Slowest
529.0ms
(- (pow -1 1/9) (+ (* 4/9 (* (pow a 2) (pow -1 1/9))) (* 4/9 (* (pow b 2) (pow -1 1/9)))))
489.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
476.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
424.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
294.0ms
(+ (* 4/9 (pow (/ 1 (pow b 14)) 1/9)) (pow (/ -1 b) -4/9))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))) (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))))
0.2b
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
147×cbrt-prod
58×add-sqr-sqrt
26×*-un-lft-identity add-cube-cbrt
16×unswap-sqr
12×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
Slowest
16.0ms
(* (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))) (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))))
2.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
2.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
2.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
354.0ms
(* (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))) (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))))
279.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
262.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
246.0ms
(cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

simplify26.1s

Counts
122 → 136
Calls
122 calls:
Slowest
666.0ms
(* (sqrt (cbrt (cbrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))) (cbrt (cbrt (sqrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))))
491.0ms
(- (pow -1 1/9) (+ (* 4/9 (* (pow a 2) (pow -1 1/9))) (* 4/9 (* (pow b 2) (pow -1 1/9)))))
485.0ms
(- (pow -1 1/9) (+ (* 4/9 (* (pow a 2) (pow -1 1/9))) (* 4/9 (* (pow b 2) (pow -1 1/9)))))
422.0ms
(- (pow -1 1/9) (+ (* 4/9 (* (pow a 2) (pow -1 1/9))) (* 4/9 (* (pow b 2) (pow -1 1/9)))))
338.0ms
(+ (* 4/9 (pow (/ 1 (pow b 14)) 1/9)) (pow (/ -1 b) -4/9))

prune3.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes340.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch11.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
4.6s20415×body80valid