Details

Time bar (total: 7.0s)

sample43.0ms

Algorithm
intervals
Results
20.0ms247×body80valid
4.0ms17×body640valid
3.0ms9×body1280valid
3.0ms13×body320valid
1.0ms9×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: 16.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.4b
(+ x (* (- y z) (/ (- t x) (- a z))))
7.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite58.0ms

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:
13.0ms
(/ (- t x) (- a z))
4.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
35.0ms
(* (- y z) (/ (- t x) (- a z)))

series337.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ (- t x) (- a z))
153.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
133.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0488901
12066849
25001847

prune357.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
2.4b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.0b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
60×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
28×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
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 145
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
85.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series750.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (- a z))
149.0ms
(cbrt (- a z))
297.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
158.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify91.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07571897
133391727
250021624

prune501.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
1.3b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
4.1b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
35×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
16×add-sqr-sqrt *-un-lft-identity
15×cbrt-prod
14×associate-*l*
10×add-cube-cbrt
9×pow1
8×times-frac
6×cbrt-div add-log-exp
5×frac-times associate-*r/
4×expm1-log1p-u log1p-expm1-u
3×flip3-- fma-def 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 → 114
Calls
4 calls:
3.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
98.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (- a z))
151.0ms
(cbrt (- a z))
301.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
160.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify80.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06432145
125211695
250021538

prune392.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cbrt (- a z)))
0.5b
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
1.3b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))
6.0b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
112×add-exp-log
52×prod-exp cbrt-unprod
51×add-cbrt-cube
35×cbrt-undiv div-exp
26×cbrt-div
19×cbrt-prod
14×add-sqr-sqrt *-un-lft-identity associate-*l*
10×add-cube-cbrt
9×pow1 frac-times
8×flip3-- times-frac flip--
7×associate-*r/
6×add-log-exp
5×associate-*l/
4×expm1-log1p-u log1p-expm1-u
3×fma-def pow-prod-down
2×pow1/3 associate-/r/ distribute-lft-out-- difference-of-squares
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 131
Calls
4 calls:
3.0ms
(cbrt (cbrt (- a z)))
8.0ms
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
154.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))
4.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

series760.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (cbrt (- a z)))
130.0ms
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
311.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))
164.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08713670
135892805
250012468

prune461.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.4b

regimes378.0ms

Accuracy

6.4% (8.1b remaining)

Error of 11.8b against oracle of 3.8b and baseline of 12.4b

bsearch64.0ms

Steps
ItersRangePoint
8
4.3121549919289474e+189
1.008355074587789e+194
7.174018341545514e+192

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03029
13029

end0.0ms

sample1.2s

Algorithm
intervals
Results
628.0ms7805×body80valid
121.0ms489×body640valid
83.0ms415×body320valid
71.0ms225×body1280valid
39.0ms288×body160valid
6.0ms16×body2560valid