Details

Time bar (total: 4.9s)

sample30.0ms

Algorithm
intervals
Results
8.0ms255×body80valid
2.0ms17×body640valid
2.0ms18×body320valid
2.0ms10×body1280valid
0.0ms5×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

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
15.3b
(fma (- y z) (/ (- t x) (- a z)) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
12.0ms
(/ (- t x) (- a z))
0.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series144.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(/ (- t x) (- a z))
91.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify54.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0268450
1733425
22490423
35001421

prune196.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.2b
(+ (* (- y z) (/ (- t x) (- a z))) x)
5.7b
(* (- y z) (/ (- t x) (- a z)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×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 log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 126
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
11.0ms
(+ (* (- y z) (/ (- t x) (- a z))) x)
32.0ms
(* (- y z) (/ (- t x) (- a z)))

series330.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ (- t x) (- a z))
148.0ms
(+ (* (- y z) (/ (- t x) (- a z))) x)
133.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0489904
12048854
25001852

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
10.3b
(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
4 → 65
Calls
4 calls:
2.0ms
(cbrt (- t x))
2.0ms
(cbrt (- t x))
2.0ms
(cbrt (- t x))
170.0ms
(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

series602.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(cbrt (- t x))
151.0ms
(cbrt (- t x))
147.0ms
(cbrt (- t x))
150.0ms
(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

simplify144.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0263766
1798659
24933604
35001604

prune345.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
11.7b
(fma (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (- t x))
2.0ms
(cbrt (- t x))
2.0ms
(cbrt (- t x))
0.0ms
(fma (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

series757.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (- t x))
147.0ms
(cbrt (- t x))
154.0ms
(cbrt (- t x))
303.0ms
(fma (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

simplify47.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0194602
1458548
21557532
35001511

prune310.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.2b

regimes363.0ms

Accuracy

14.6% (7.4b remaining)

Error of 10.8b against oracle of 3.4b and baseline of 12.0b

bsearch65.0ms

Steps
ItersRangePoint
3
1.829737677608388e-73
2.20669767931691e-73
1.9946576783558662e-73
7
-1.0411090379625735e-32
-7.240415757318844e-35
-7.37556037696158e-35

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03023
13023

end0.0ms

sample702.0ms

Algorithm
intervals
Results
266.0ms7854×body80valid
59.0ms463×body640valid
41.0ms439×body320valid
40.0ms238×body1280valid
18.0ms293×body160valid
4.0ms19×body2560valid