Details

sample163.0ms

Algorithm

intervals

Results

81.0ms	1805×	body	80	nan
14.0ms	258×	body	80	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	61	8
2	161	8
3	393	8
4	984	8
5	2256	8
6	4095	8
7	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
7×	`pow1` `log-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `log-pow` `distribute-lft-out`
4×	`associate-+l+` `fma-def`
3×	`associate-+r+`
2×	`add-exp-log` `expm1-log1p-u` `associate-+l-` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

2 → 40

Calls

2 calls:

0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
6.0ms	(+ (log (+ x y)) (log z))

series168.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
73.0ms	(+ (log (+ x y)) (log z))

simplify58.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	262	323
1	662	288
2	2590	282
3	5001	278

prune196.0ms

Filtered

46 candidates to 38 candidates (82.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.5b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-+r+` `log-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/3` `fma-udef` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `log-pow` `flip-+`

Counts

4 → 61

Calls

4 calls:

4.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
0.0ms	(cbrt z)
1.0ms	(cbrt z)

series667.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
137.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
175.0ms	(cbrt z)
180.0ms	(cbrt z)

simplify70.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	203	445
1	573	409
2	2204	368
3	5002	358

prune394.0ms

Filtered

73 candidates to 67 candidates (91.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.6b	(cbrt (* (cbrt z) (cbrt z)))
0.6b	(cbrt (cbrt z))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 53

Calls

4 calls:

0.0ms	(cbrt z)
0.0ms	(cbrt z)
2.0ms	(cbrt (* (cbrt z) (cbrt z)))
1.0ms	(cbrt (cbrt z))

series872.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt z)
178.0ms	(cbrt z)
274.0ms	(cbrt (* (cbrt z) (cbrt z)))
242.0ms	(cbrt (cbrt z))

simplify103.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (99.0ms)

Iter	Nodes	Cost
0	112	239
1	242	219
2	759	209
3	3150	209
4	5001	204

prune426.0ms

Filtered

65 candidates to 58 candidates (89.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
0.5b	(cbrt (pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3))
0.5b	(fma 2/3 (log z) (log (+ x y)))
0.7b	(pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

0.0ms	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
1.0ms	(cbrt (pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3))
0.0ms	(fma 2/3 (log z) (log (+ x y)))
1.0ms	(pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3)

series627.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
115.0ms	(cbrt (pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3))
93.0ms	(fma 2/3 (log z) (log (+ x y)))
310.0ms	(pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3)

simplify176.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (167.0ms)

Iter	Nodes	Cost
0	204	707
1	686	652
2	4621	632
3	5001	625

prune334.0ms

Filtered

80 candidates to 59 candidates (73.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes574.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	56141×	body	80	nan
439.0ms	8025×	body	80	valid