Details

sample75.0ms

Algorithm

intervals

Results

26.0ms	369×	body	80	valid
25.0ms	345×	body	80	nan

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (19.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 5.2b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
75×	`add-cube-cbrt`
74×	`prod-diff`
64×	`times-frac`
16×	`distribute-lft-out--`
15×	`difference-of-squares`
13×	`fma-neg`
11×	`associate--r+`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`sub-neg` `associate-*l/` `frac-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

23.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series321.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
37.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
120.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify99.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	737	3116
1	2431	2540
2	5002	2408

prune485.0ms

Filtered

186 candidates to 111 candidates (59.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	8	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Merged error: 2.8b

Counts

188 → 9

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)) x)
0.2b	(* (- x 0.5) (log x))
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

430.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
414.0ms	(- (* (- x 0.5) (log x)) x)
255.0ms	(* (- x 0.5) (log x))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	576	925
1	2275	825
2	5001	802

prune395.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	126	11	137

Merged error: 2.8b

Counts

137 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `flip3--` `frac-add` `flip--` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

14.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

779.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
183.0ms	(cbrt x)
222.0ms	(cbrt x)
112.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify78.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	680	1100
1	2677	947
2	5001	914

prune653.0ms

Filtered

124 candidates to 113 candidates (91.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	3	6	9
Picked	0	1	1
Done	1	0	1
Total	126	9	135

Merged error: 2.8b

Counts

135 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (cbrt x))
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
4.9b	(pow x 1/3)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt (cbrt x))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
2.0ms	(pow x 1/3)

series664.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt x)
237.0ms	(cbrt (cbrt x))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
171.0ms	(pow x 1/3)

simplify38.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	314	526
1	1141	467
2	5002	460

prune510.0ms

Filtered

92 candidates to 77 candidates (83.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Merged error: 2.8b

Counts

101 → 9

regimes386.0ms

Accuracy

66.5% (1.0b remaining)

Error of 4.1b against oracle of 3.1b and baseline of 6.0b

bsearch92.0ms

Steps

Iters	Range		Point
8	3149248628356.163	5.824440241286023e+16	405675084276533.1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	33
1	53	33

end0.0ms

sample2.1s

Algorithm

intervals

Results

827.0ms	11629×	body	80	valid
734.0ms	11595×	body	80	nan

Details

sample75.0ms

simplify64.0ms

prune10.0ms

localize17.0ms

rewrite52.0ms

series321.0ms

simplify99.0ms

prune485.0ms

localize17.0ms

rewrite40.0ms

series1.2s

simplify67.0ms

prune395.0ms

localize22.0ms

rewrite32.0ms

series1.3s

simplify78.0ms

prune653.0ms

localize40.0ms

rewrite18.0ms

series664.0ms

simplify38.0ms

prune510.0ms

regimes386.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling