Details

Time bar (total: 9.5s)

sample35.0ms

Algorithm
intervals
Results
17.0ms492×body80valid

simplify91.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 9 (76.0ms)

IterNodesCost
0216
1526
21716
34016
48296
510906
616106
719566
822526
923675
1023675

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* z z) t)
0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.7b
(* (* y 4.0) (- (* z z) t))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
16×prod-diff
11×add-sqr-sqrt
10×distribute-rgt-in distribute-lft-in associate--r+
9×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
7×add-log-exp
6×sub-neg
4×associate-*r*
3×expm1-log1p-u flip3-- pow-prod-down prod-exp flip-- cbrt-unprod log1p-expm1-u
2×fma-neg diff-log associate-*r/ difference-of-squares
1×associate-*l* *-commutative
Counts
3 → 78
Calls
3 calls:
9.0ms
(- (* z z) t)
11.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
40.0ms
(* (* y 4.0) (- (* z z) t))

series150.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(- (* z z) t)
71.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
59.0ms
(* (* y 4.0) (- (* z z) t))

simplify57.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0412584
11842481
25002472

prune295.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.5b

localize18.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))) (cbrt (- (* z z) t))))
6.2b
(cbrt (- (* z z) t))
6.2b
(cbrt (- (* z z) t))
6.2b
(cbrt (- (* z z) t))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
34×associate-*r/
30×flip3-- flip--
28×frac-times
25×pow1 add-exp-log
17×add-cbrt-cube
15×pow-prod-down prod-exp cbrt-unprod
14×associate-*l/
12×cbrt-prod
10×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 difference-of-squares
1×associate-*r* associate-*l* *-commutative
Counts
4 → 104
Calls
4 calls:
282.0ms
(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))) (cbrt (- (* z z) t))))
6.0ms
(cbrt (- (* z z) t))
7.0ms
(cbrt (- (* z z) t))
7.0ms
(cbrt (- (* z z) t))

series312.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))) (cbrt (- (* z z) t))))
91.0ms
(cbrt (- (* z z) t))
82.0ms
(cbrt (- (* z z) t))
84.0ms
(cbrt (- (* z z) t))

simplify52.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05021361
115381098
250011024

prune849.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.5b

localize12.0ms

Local error

Found 4 expressions with local error:

2.7b
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
2.7b
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
5.7b
(* (* y 4.0) (- (* z z) t))
5.7b
(* (* y 4.0) (- (* z z) t))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
8×associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg flip3-- sqrt-div associate-*r/ flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative difference-of-squares
Counts
4 → 100
Calls
4 calls:
12.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
11.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
37.0ms
(* (* y 4.0) (- (* z z) t))
39.0ms
(* (* y 4.0) (- (* z z) t))

series378.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
128.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
61.0ms
(* (* y 4.0) (- (* z z) t))
56.0ms
(* (* y 4.0) (- (* z z) t))

simplify55.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0352866
11571746
25001742

prune620.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

6.2b
(cbrt (- (* z z) t))
8.4b
(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* (* z z) (* z z)) (* t t)))) (cbrt (- (* z z) t))))
9.8b
(/ (* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* (* z z) (* z z)) (* t t)))) (cbrt (- (* z z) t)))) (cbrt (+ (* z z) t)))
29.2b
(cbrt (- (* (* z z) (* z z)) (* t t)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
114×cbrt-div
68×associate-*r/
56×frac-times flip3-- flip--
54×add-exp-log
31×add-cbrt-cube
30×prod-exp cbrt-unprod
28×associate-*l/
26×associate-/l/
25×pow1
15×pow-prod-down
14×cbrt-prod
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×cbrt-undiv div-exp
6×times-frac associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow1/3 associate-/r/ difference-of-squares
1×frac-2neg flip3-+ associate-*r* associate-*l* clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 155
Calls
4 calls:
7.0ms
(cbrt (- (* z z) t))
587.0ms
(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* (* z z) (* z z)) (* t t)))) (cbrt (- (* z z) t))))
519.0ms
(/ (* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* (* z z) (* z z)) (* t t)))) (cbrt (- (* z z) t)))) (cbrt (+ (* z z) t)))
33.0ms
(cbrt (- (* (* z z) (* z z)) (* t t)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(cbrt (- (* z z) t))
137.0ms
(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* (* z z) (* z z)) (* t t)))) (cbrt (- (* z z) t))))
159.0ms
(/ (* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* (* z z) (* z z)) (* t t)))) (cbrt (- (* z z) t)))) (cbrt (+ (* z z) t)))
89.0ms
(cbrt (- (* (* z z) (* z z)) (* t t)))

simplify102.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08693165
133372767
250022708

prune2.6s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 2.5b

regimes697.0ms

Accuracy

60.8% (1.3b remaining)

Error of 4.2b against oracle of 2.9b and baseline of 6.2b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02516
12516

end0.0ms

sample1.0s

Algorithm
intervals
Results
580.0ms15774×body80valid