Details

analyze2.0ms

Algorithm: search

sample101.0ms

Algorithm

intervals

Results

49.0ms	137×	body	1280	valid
26.0ms	28×	body	2560	valid
14.0ms	61×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

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: 37.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.0b	(cos (+ x eps))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

12.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series15.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
6.0ms	(cos (+ x eps))

simplify109.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune79.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	17	13	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	13	31

Merged error: 17.0b

Counts

31 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
3.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series59.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
26.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify114.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune148.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	67	15	82
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	76	19	95

Merged error: 16.9b

Counts

95 → 19

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
0.2b	(* (sin x) (sin eps))
3.3b	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
4.6b	(log (exp (* (sin x) (sin eps))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

5.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
4.0ms	(* (sin x) (sin eps))
8.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
2.0ms	(log (exp (* (sin x) (sin eps))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps)))))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
9.0ms	(log (exp (* (sin x) (sin eps))))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	266	688
1	792	625
2	3018	609
3	5001	609

prune127.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	18	18
Picked	0	1	1
Done	0	0	0
Total	78	19	97

Merged error: 16.9b

Counts

97 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
0.4b	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
3.7b	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
30×	`add-exp-log` `add-cbrt-cube`
23×	`cos-mult` `sin-mult`
18×	`add-sqr-sqrt`
16×	`prod-exp` `cbrt-unprod` `associate-/l/`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
12×	`associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp` `difference-of-squares`
5×	`sub-div`
4×	`pow-plus` `associate-/l*`
3×	`associate-/r*` `associate-/r/`
2×	`pow2` `flip3--` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--`
1×	`cbrt-undiv` `associate--l-` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-add` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 141

Calls

4 calls:

9.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
18.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
8.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
17.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

series177.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
57.0ms	(/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps))))
12.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
95.0ms	(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))

simplify98.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	620	2406
1	3205	2128
2	5002	2122

prune157.0ms

Filtered

94 candidates to 153 candidates (-62.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	144	9	153
Fresh	6	11	17
Picked	1	0	1
Done	1	0	1
Total	152	20	172

Merged error: 16.8b

Counts

172 → 20

regimes284.0ms

Accuracy

76.8% (2.2b remaining)

Error of 16.7b against oracle of 14.5b and baseline of 24.2b

bsearch105.0ms

Steps

Iters	Range		Point
6	3.823720437665534e-10	5.702397994995682e-09	2.8465589353104773e-09
10	-1.2787307292350069e-36	-6.882720814028008e-52	-1.2601176313428123e-36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	39
1	48	39

end0.0ms

analyze1.0ms

Algorithm: search

sample3.0s

Algorithm

intervals

Results

1.7s	4475×	body	1280	valid
551.0ms	599×	body	2560	valid
431.0ms	1844×	body	640	valid
114.0ms	729×	body	320	valid
31.0ms	276×	body	160	valid
4.0ms	77×	body	80	valid

Details

analyze2.0ms

sample101.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite16.0ms

series15.0ms

simplify109.0ms

prune79.0ms

localize14.0ms

rewrite23.0ms

series59.0ms

simplify114.0ms

prune148.0ms

localize17.0ms

rewrite21.0ms

series59.0ms

simplify80.0ms

prune127.0ms

localize18.0ms

rewrite60.0ms

series177.0ms

simplify98.0ms

prune157.0ms

regimes284.0ms

bsearch105.0ms

simplify2.0ms

end0.0ms

analyze1.0ms

sample3.0s

Profiling