Details

sample102.0ms

Algorithm

intervals

Results

25.0ms	51×	body	10240	exit
24.0ms	48×	body	1280	valid
14.0ms	51×	body	640	valid
7.0ms	125×	body	80	valid
4.0ms	21×	body	320	valid
3.0ms	88×	body	80	nan
3.0ms	2×	body	2560	valid
2.0ms	9×	body	640	nan
1.0ms	10×	body	160	valid
1.0ms	4×	body	1280	nan
1.0ms	5×	body	320	nan
0.0ms	2×	body	160	nan

simplify217.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 24.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.5b	(log (+ (- 1.0 y) (* y (exp z))))
3.2b	(+ (- 1.0 y) (* y (exp z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
158.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
77.0ms	(log (+ (- 1.0 y) (* y (exp z))))
35.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune454.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 4.2b

Counts

115 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
4.0b	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
18.4b	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1`
10×	`swap-sqr`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `flip3--` `pow1/3` `flip--` `distribute-lft-out--`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`log-prod`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 99

Calls

4 calls:

6.0ms	(cbrt (- 1.0 y))
10.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
1.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
1.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

series838.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (- 1.0 y))
293.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
254.0ms	(log (fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z))))
201.0ms	(fma (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y))) (cbrt (- 1.0 y)) (* y (exp z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	517	1081
1	1755	983
2	5002	917

prune398.0ms

Filtered

111 candidates to 82 candidates (73.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	111	6	117

Merged error: 4.2b

Counts

117 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.3b	(/ (* z y) t)
6.4b	(/ (* (pow z 2) y) t)
8.2b	(* (pow z 2) y)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

1.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.0ms	(/ (* z y) t)
5.0ms	(/ (* (pow z 2) y) t)
5.0ms	(* (pow z 2) y)

series148.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
21.0ms	(/ (* z y) t)
18.0ms	(/ (* (pow z 2) y) t)
17.0ms	(* (pow z 2) y)

simplify45.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	300	473
1	1353	406
2	5002	406

prune323.0ms

Filtered

99 candidates to 68 candidates (68.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 3.5b

Counts

105 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (* (* z y) (/ 1 t)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.4b	(* (* z y) (/ 1 t))
6.4b	(/ (* (pow z 2) y) t)
8.2b	(* (pow z 2) y)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`add-sqr-sqrt`
18×	`prod-exp`
16×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
12×	`times-frac`
9×	`pow1` `associate-l`
8×	`div-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `*-commutative` `div-inv` `unpow2` `sqr-pow`
1×	`frac-2neg` `associate-r/` `clear-num` `un-div-inv` `fma-udef` `associate-/l`

Counts

4 → 104

Calls

4 calls:

1.0ms	(fma (* (* z y) (/ 1 t)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
8.0ms	(* (* z y) (/ 1 t))
5.0ms	(/ (* (pow z 2) y) t)
5.0ms	(* (pow z 2) y)

series150.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (* (* z y) (/ 1 t)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
19.0ms	(* (* z y) (/ 1 t))
18.0ms	(/ (* (pow z 2) y) t)
22.0ms	(* (pow z 2) y)

simplify67.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	447	586
1	2338	487
2	5001	473

prune337.0ms

Filtered

116 candidates to 73 candidates (62.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	117	10	127

Merged error: 3.5b

Counts

127 → 10

regimes485.0ms

Accuracy

70.1% (5.1b remaining)

Error of 8.6b against oracle of 3.5b and baseline of 20.5b

bsearch86.0ms

Steps

Iters	Range		Point
9	-1.4365382038701608e-08	-5.490563833332279e-14	-1.2015657265463743e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms

sample3.1s

Algorithm

intervals

Results

751.0ms	1407×	body	1280	valid
737.0ms	1480×	body	10240	exit
475.0ms	1595×	body	640	valid
218.0ms	3566×	body	80	valid
163.0ms	888×	body	320	valid
102.0ms	2530×	body	80	nan
100.0ms	80×	body	2560	valid
56.0ms	486×	body	160	valid
55.0ms	279×	body	640	nan
34.0ms	120×	body	1280	nan
26.0ms	193×	body	320	nan
10.0ms	119×	body	160	nan