Details

sample89.0ms

Algorithm

intervals

Results

44.0ms	133×	body	1280	valid
19.0ms	22×	body	2560	valid
14.0ms	67×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize13.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.0b	(cos (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune91.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

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)))
0.1b	(* (sin x) (sin eps))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite33.0ms

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:

3.0ms	(* (cos x) (cos eps))
5.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms	(* (sin x) (sin eps))
20.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series306.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (cos eps))
84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
44.0ms	(* (sin x) (sin eps))
133.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify115.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	304	633
1	1061	602
2	4487	583
3	5002	583

prune249.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (sin eps))
0.2b	(pow (* (sin x) (sin eps)) 3)
2.4b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
28.5b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
3.0ms	(pow (* (sin x) (sin eps)) 3)
43.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
2.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series300.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin x) (sin eps))
64.0ms	(pow (* (sin x) (sin eps)) 3)
137.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
47.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	293	634
1	1142	580
2	5001	565

prune293.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 13.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))) (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))))
0.3b	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
0.3b	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
2.4b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cos-mult` `frac-sub`
24×	`associate-/l/`
22×	`flip3--` `flip--`
19×	`add-log-exp`
16×	`frac-times`
9×	`add-exp-log` `add-cbrt-cube`
8×	`diff-log`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
5×	`sub-neg` `associate--r+`
4×	`pow1` `associate-r/` `associate-l/` `associate-/r/`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate--r-`
1×	`frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 101

Calls

4 calls:

55.0ms	(/ (* (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))) (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))))
10.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
10.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
9.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (* (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))) (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))) (- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x))))
107.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
102.0ms	(- (* (cos x) (cos eps)) (- (* (sin x) (sin eps)) (cos x)))
138.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	687	2757
1	4435	2485
2	5001	2355

prune470.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.3b

regimes241.0ms

Accuracy

86.1% (1.4b remaining)

Error of 16.1b against oracle of 14.7b and baseline of 24.5b

bsearch123.0ms

Steps

Iters	Range		Point
8	9.143643357499823e-08	5.968040026638966e-05	2.2379838828549683e-07
7	-9.091202463712598e-16	-2.574374193275519e-17	-8.911882491803393e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	38
1	44	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4457×	body	1280	valid
587.0ms	686×	body	2560	valid
414.0ms	1837×	body	640	valid
94.0ms	656×	body	320	valid
29.0ms	292×	body	160	valid
4.0ms	72×	body	80	valid