Details

sample78.0ms

Algorithm

intervals

Results

28.0ms	381×	body	80	valid
26.0ms	450×	body	80	nan

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

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: 5.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

446.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
261.0ms	(* (- x 0.5) (log x))
439.0ms	(- (* (- x 0.5) (log x)) x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	501	839
1	1642	776
2	5002	763

prune378.0ms

Filtered

110 candidates to 84 candidates (76.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 4.3b

Counts

111 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
15.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series660.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt x)
187.0ms	(cbrt x)
187.0ms	(cbrt x)
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify102.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	212	462
1	697	420
2	3307	413
3	5001	410

prune495.0ms

Filtered

74 candidates to 62 candidates (83.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 4.3b

Counts

83 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x)
0.5b	(* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x))))
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

56×	`pow1`
28×	`sqrt-pow1`
27×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`pow-prod-down`
20×	`add-cube-cbrt`
16×	`associate-*l/`
12×	`sqrt-div`
10×	`add-exp-log` `pow1/2` `pow-prod-up` `add-cbrt-cube`
9×	`times-frac` `associate-l`
8×	`flip3--` `associate-r` `flip--`
6×	`log-prod` `pow-sqr` `add-log-exp`
4×	`frac-times` `swap-sqr` `sqrt-prod`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/r` `associate-/l`
2×	`associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `diff-log` `div-exp` `clear-num` `rem-square-sqrt` `log-pow` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 128

Calls

4 calls:

7.0ms	(* (- x 0.5) (log x))
15.0ms	(- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x)
14.0ms	(* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x))))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series981.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (- x 0.5) (log x))
348.0ms	(- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x)
283.0ms	(* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x))))
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify102.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	830	1324
1	3882	1181
2	5002	1158

prune431.0ms

Filtered

140 candidates to 86 candidates (61.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Merged error: 4.3b

Counts

149 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (log x)) x)
0.3b	(/ 1 (sqrt x))
1.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
3.8b	(* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
94×	`times-frac`
68×	`*-un-lft-identity`
62×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `log-prod` `associate--l+` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod` `div-inv`
3×	`distribute-rgt-in` `rec-exp` `pow-flip` `distribute-lft-in` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

7.0ms	(- (* (- x 0.5) (log x)) x)
4.0ms	(/ 1 (sqrt x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
23.0ms	(* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

433.0ms	(- (* (- x 0.5) (log x)) x)
187.0ms	(/ 1 (sqrt x))
99.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
111.0ms	(* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)))

simplify101.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	798	2206
1	4435	1968
2	5002	1870

prune489.0ms

Filtered

199 candidates to 119 candidates (59.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	199	9	208

Merged error: 4.3b

Counts

208 → 9

regimes297.0ms

Accuracy

75.7% (0.3b remaining)

Error of 5.2b against oracle of 4.9b and baseline of 6.3b

bsearch99.0ms

Steps

Iters	Range		Point
8	2.4349687922908843e+132	1.933236461977481e+136	3.138825795002145e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	30
1	56	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

760.0ms	11638×	body	80	valid
658.0ms	11581×	body	80	nan

Details

sample78.0ms

simplify55.0ms

prune3.0ms

localize17.0ms

rewrite41.0ms

series1.2s

simplify50.0ms

prune378.0ms

localize23.0ms

rewrite21.0ms

series660.0ms

simplify102.0ms

prune495.0ms

localize21.0ms

rewrite52.0ms

series981.0ms

simplify102.0ms

prune431.0ms

localize24.0ms

rewrite54.0ms

series831.0ms

simplify101.0ms

prune489.0ms

regimes297.0ms

bsearch99.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling