Details

sample520.0ms

Algorithm

intervals

Results

135.0ms	58×	body	2560	valid
58.0ms	91×	body	1280	valid
12.0ms	49×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	12×	body	80	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune5.0ms

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: 33.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.5b	(- x (sin x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series179.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
61.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify156.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune167.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Merged error: 0.0b

Counts

90 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 27/2800 (pow x 4)) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
13.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `associate--r+`

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
5.0ms	(* 27/2800 (pow x 4))
9.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series196.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
41.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	316	412
1	1299	379
2	5002	374

prune150.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	89	2	91

Merged error: 0b

Counts

91 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
13.6b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `diff-log` `sqr-pow`
3×	`sub-neg`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unpow2`
1×	`associate--l-` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

10.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
43.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
111.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	308	474
1	1219	442
2	5001	431

prune155.0ms

Filtered

94 candidates to 59 candidates (62.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	94	2	96

Merged error: 0b

Counts

96 → 2

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.5b

bsearch72.0ms

Steps

Iters	Range		Point
9	0.004314681149180372	39972.03059165128	0.02515968471535556
9	-2.6022242175013632	-1.4174312616962401e-08	-0.029786027982061425

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.0s	1614×	body	2560	valid
1.7s	2786×	body	1280	valid
443.0ms	1815×	body	640	valid
150.0ms	922×	body	320	valid
60.0ms	514×	body	160	valid
31.0ms	349×	body	80	valid

Details

sample520.0ms

simplify34.0ms

prune5.0ms

localize11.0ms

rewrite21.0ms

series179.0ms

simplify156.0ms

prune167.0ms

localize10.0ms

rewrite27.0ms

series196.0ms

simplify48.0ms

prune150.0ms

localize10.0ms

rewrite26.0ms

series225.0ms

simplify51.0ms

prune155.0ms

regimes43.0ms

bsearch72.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling