Details

Time bar (total: 8.6s)

sample27.0ms

Algorithm
intervals
Results
7.0ms248×body80valid
2.0ms23×body640valid
1.0ms11×body320valid
1.0ms6×body1280valid
0.0ms5×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0206
1456
21116
32886
47146
514986
634106
750016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- y z) (- t x))
0.9b
(+ x (/ (* (- y z) (- t x)) (- a z)))
15.8b
(/ (* (- y z) (- t x)) (- a z))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
13×flip3-- flip--
10×add-exp-log add-cbrt-cube
8×frac-times associate-/l/
7×add-cube-cbrt
5×pow1 times-frac associate-*r* associate-*l* associate-/r* add-log-exp
4×associate-*r/ associate-*l/ distribute-lft-out-- difference-of-squares
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in div-exp prod-exp associate-/r/ cbrt-unprod
1×+-commutative frac-2neg flip3-+ pow-prod-down clear-num sum-log *-commutative flip-+ div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
3 → 81
Calls
3 calls:
41.0ms
(* (- y z) (- t x))
21.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
33.0ms
(/ (* (- y z) (- t x)) (- a z))

series276.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(* (- y z) (- t x))
131.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
112.0ms
(/ (* (- y z) (- t x)) (- a z))

simplify55.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0466583
12158534
25001534

prune227.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.9b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.8b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
59×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 134
Calls
4 calls:
4.0ms
(cbrt (- a z))
4.0ms
(cbrt (- a z))
138.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series673.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(cbrt (- a z))
131.0ms
(cbrt (- a z))
270.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
139.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify82.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07441831
132871663
250011576

prune420.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.0b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.6b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
35×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
15×cbrt-prod add-sqr-sqrt *-un-lft-identity
14×associate-*l*
9×pow1 add-cube-cbrt
8×times-frac
6×cbrt-div add-log-exp
5×frac-times associate-*r/
3×flip3-- pow-prod-down associate-*l/ flip-- distribute-lft-out-- difference-of-squares
2×pow1/3 associate-/r/
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 103
Calls
4 calls:
4.0ms
(cbrt (- a z))
4.0ms
(cbrt (- a z))
158.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
9.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series670.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (- a z))
135.0ms
(cbrt (- a z))
262.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
139.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify72.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06302051
124661604
250011462

prune337.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
1.1b
(* (/ (cbrt (- y z)) (cbrt (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
5.5b
(+ x (* (/ (cbrt (- y z)) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (/ (cbrt (- y z)) (cbrt (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
165×cbrt-prod
94×associate-*l*
92×add-sqr-sqrt *-un-lft-identity
88×times-frac
52×add-cube-cbrt
45×add-exp-log
26×cbrt-div
23×add-cbrt-cube
20×distribute-lft-out-- difference-of-squares
18×prod-exp cbrt-unprod
13×cbrt-undiv div-exp
9×pow1 frac-times
8×flip3-- flip--
7×associate-*r/
6×add-log-exp
5×associate-*l/
3×pow-prod-down
2×pow1/3 associate-/r/
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 175
Calls
4 calls:
4.0ms
(cbrt (- a z))
14.0ms
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
154.0ms
(* (/ (cbrt (- y z)) (cbrt (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
14.0ms
(+ x (* (/ (cbrt (- y z)) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (/ (cbrt (- y z)) (cbrt (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))))

series2.7s

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (- a z))
118.0ms
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
2.3s
(* (/ (cbrt (- y z)) (cbrt (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
143.0ms
(+ x (* (/ (cbrt (- y z)) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (/ (cbrt (- y z)) (cbrt (cbrt (- a z)))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))))

simplify108.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
09223477
133853152
250013107

prune811.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

regimes465.0ms

Accuracy

1.6% (8.3b remaining)

Error of 12.3b against oracle of 4.0b and baseline of 12.5b

bsearch155.0ms

Steps
ItersRangePoint
8
9.435024383722458e+37
2.4178810551420217e+40
9.567966369800805e+37
9
3.155539273665743e-74
1.8614563384609176e-67
7.235207005480106e-71
3
1.30504018262409e-204
1.5453155670988291e-204
1.5002639325098155e-204
7
-6.807625041097322e-136
-4.9000185529713867e-138
-1.0584862439221319e-137

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 2 (1.0ms)

IterNodesCost
04472
14772
25326
35626
46226
57326
68026
78126
88126

end0.0ms

sample794.0ms

Algorithm
intervals
Results
249.0ms7738×body80valid
58.0ms499×body640valid
37.0ms268×body1280valid
36.0ms428×body320valid
15.0ms256×body160valid
3.0ms16×body2560valid