Details

Time bar (total: 35.1s)

sample149.0ms

Algorithm
intervals
Results
43.0ms104×body160valid
33.0ms119×body320valid
23.0ms526×pre80true
22.0ms270×body80nan
4.0ms12×body640valid
2.0ms21×body80valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
140.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize25.0ms

Local error

Found 4 expressions with local error:

28.3b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.0b
(sqrt (fma -3 (* c a) (* b b)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
26.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
102.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
97.0ms
(sqrt (fma -3 (* c a) (* b b)))
76.0ms
(fma -3 (* c a) (* b b))

simplify4.5s

Counts
87 → 114
Calls
87 calls:
Slowest
550.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
335.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
266.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
222.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 3) 3) (* (* a a) a)))
153.0ms
(- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (+ (log 3) (log a)))

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 49.9b

localize39.0ms

Local error

Found 4 expressions with local error:

52.9b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.3b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(fma -3 (* c a) (* b b))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac fma-udef associate-/l*
2×cbrt-undiv div-exp
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 57
Calls
4 calls:
Slowest
7.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
576.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
441.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
86.0ms
(fma -3 (* c a) (* b b))
71.0ms
(fma -3 (* c a) (* b b))

simplify2.8s

Counts
24 → 69
Calls
24 calls:
Slowest
415.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
326.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
261.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
261.0ms
(/ (* (* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
231.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune1.0s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 49.8b

localize65.0ms

Local error

Found 4 expressions with local error:

52.9b
(fma (sqrt (sqrt (* (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))) (cbrt (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.5b
(* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))
0.5b
(cbrt (fma -3 (* c a) (* b b)))
0.5b
(cbrt (fma -3 (* c a) (* b b)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×pow1
8×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 fma-udef
Counts
4 → 82
Calls
4 calls:
Slowest
21.0ms
(* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))) (cbrt (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
462.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))) (cbrt (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
283.0ms
(cbrt (fma -3 (* c a) (* b b)))
268.0ms
(* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))
250.0ms
(cbrt (fma -3 (* c a) (* b b)))

simplify5.0s

Counts
62 → 94
Calls
62 calls:
Slowest
625.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
304.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
294.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
291.0ms
(- (pow b 4/3) (* 2 (* (* a c) (pow (/ 1 (pow b 2)) 1/3))))
275.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))

prune2.0s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 49.8b

localize103.0ms

Local error

Found 4 expressions with local error:

52.7b
(fma (sqrt (sqrt (* (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))) (pow (fma -3 (* c a) (* b b)) 1/3)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
3.0b
(pow (fma -3 (* c a) (* b b)) 1/3)
0.5b
(* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))
0.5b
(cbrt (fma -3 (* c a) (* b b)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×cbrt-prod
15×*-un-lft-identity add-cube-cbrt
12×pow1
7×pow1/3 add-exp-log
6×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow unpow-prod-down
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-to-exp pow-pow pow-plus unpow1/3 pow-exp prod-exp *-commutative cbrt-unprod fma-udef sqr-pow
Counts
4 → 89
Calls
4 calls:
Slowest
16.0ms
(* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))
4.0ms
(pow (fma -3 (* c a) (* b b)) 1/3)
1.0ms
(cbrt (fma -3 (* c a) (* b b)))
1.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))) (pow (fma -3 (* c a) (* b b)) 1/3)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
357.0ms
(fma (sqrt (sqrt (* (* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b)))) (pow (fma -3 (* c a) (* b b)) 1/3)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
283.0ms
(cbrt (fma -3 (* c a) (* b b)))
278.0ms
(* (cbrt (fma -3 (* c a) (* b b))) (cbrt (fma -3 (* c a) (* b b))))
208.0ms
(pow (fma -3 (* c a) (* b b)) 1/3)

simplify5.0s

Counts
66 → 101
Calls
66 calls:
Slowest
332.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
326.0ms
(- (pow b 4/3) (* 2 (* (* a c) (pow (/ 1 (pow b 2)) 1/3))))
320.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
276.0ms
(exp (* 1/3 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c))))))
275.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))

prune1.5s

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 49.7b

regimes1.1s

Accuracy

0% (1.8b remaining)

Error of 50.7b against oracle of 48.9b and baseline of 50.7b

bsearch10.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
1.9s3645×body320valid
1.2s2958×body160valid
1.1s8129×body80nan
1.1s16129×pre80true
339.0ms478×body640valid
173.0ms919×body80valid