Details

Time bar (total: 17.8s)

sample33.0ms

Algorithm
intervals
Results
14.0ms253×body80valid
2.0ms16×body640valid
2.0ms14×body320valid
1.0ms6×body1280valid
1.0ms8×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
2.9b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.8b
(* (- y z) (/ (- t x) (- a z)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u fma-def log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 128
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
31.0ms
(* (- y z) (/ (- t x) (- a z)))

series334.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(/ (- t x) (- a z))
148.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
133.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0488901
12066849
25001847

prune364.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.2b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.0b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
34×*-un-lft-identity
33×cbrt-prod
26×cbrt-div
24×add-exp-log
21×associate-*r*
16×add-cube-cbrt
15×flip3-- flip--
14×add-cbrt-cube
13×pow1 associate-*l*
10×frac-times swap-sqr prod-exp cbrt-unprod
8×associate-/r/ distribute-lft-out--
7×pow1/3
6×associate-*l/ add-log-exp difference-of-squares unswap-sqr
5×associate-*r/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def pow-prod-down
2×times-frac pow-sqr *-commutative pow-prod-up
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+ div-inv
Counts
4 → 137
Calls
4 calls:
2.0ms
(cbrt (- a z))
20.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
58.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series723.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(cbrt (- a z))
127.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
286.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
155.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07881782
135431551
250011434

prune536.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.2b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
10.1b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
33×cbrt-prod *-un-lft-identity
26×cbrt-div
24×add-exp-log
21×associate-*r*
15×add-cube-cbrt flip3-- flip--
14×add-cbrt-cube
13×pow1 associate-*l*
10×frac-times swap-sqr prod-exp cbrt-unprod
8×associate-/r/ distribute-lft-out--
7×pow1/3
6×associate-*l/ difference-of-squares unswap-sqr
5×associate-*r/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×pow-prod-down
2×times-frac pow-sqr *-commutative pow-prod-up
1×pow2 pow-plus fma-udef div-inv
Counts
4 → 131
Calls
4 calls:
2.0ms
(cbrt (- a z))
19.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
56.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(cbrt (- a z))
126.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
281.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
164.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify91.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07251685
132181477
250021401

prune577.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.2b
(* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
10.2b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
40×cbrt-prod
34×*-un-lft-identity
30×cbrt-div
24×add-exp-log
21×associate-*r*
16×add-cube-cbrt associate-*l*
15×flip3-- flip--
13×pow1
10×frac-times swap-sqr prod-exp cbrt-unprod
9×add-cbrt-cube
8×associate-/r/ distribute-lft-out-- unswap-sqr
7×pow1/3
6×associate-*l/ difference-of-squares
5×associate-*r/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac pow-prod-down
2×pow-sqr *-commutative pow-prod-up
1×pow2 pow-plus fma-udef div-inv
Counts
4 → 136
Calls
4 calls:
2.0ms
(cbrt (- a z))
19.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
58.0ms
(* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series11.4s

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (- a z))
125.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
10.9s
(* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
161.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07091878
129531683
250011608

prune648.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.5b

regimes451.0ms

Accuracy

15% (7.3b remaining)

Error of 10.9b against oracle of 3.6b and baseline of 12.2b

bsearch278.0ms

Steps
ItersRangePoint
10
2.4894908659714922e-216
8.28527612461248e-205
1.6198574735816835e-205
9
-1.7557548994774836e-131
-1.3702607488594748e-138
-1.1082483719169987e-137
9
-1.8821136628682014e-107
-1.9176345575095877e-112
-1.860109821827876e-107
8
-3.5916787608831703e-51
-7.178944096305044e-56
-7.303074110842033e-56

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05498
15498

end0.0ms

sample962.0ms

Algorithm
intervals
Results
466.0ms7810×body80valid
77.0ms466×body640valid
56.0ms287×body1280valid
50.0ms402×body320valid
26.0ms287×body160valid
3.0ms13×body2560valid