Details

sample92.0ms

Algorithm

intervals

Results

41.0ms	110×	body	1280	valid
18.0ms	22×	body	2560	valid
11.0ms	52×	body	640	valid
8.0ms	28×	body	320	valid
1.0ms	32×	body	80	valid
1.0ms	12×	body	160	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

prune4.0ms

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: 36.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (tan (+ x eps)) (tan x))
3.7b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune123.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	23	8	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	8	32

Merged error: 14.3b

Counts

32 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
15.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series751.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan x) (tan eps))
354.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	397	1052
1	1432	1007
2	5001	995

prune412.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	89	17	106

Merged error: 14.2b

Counts

106 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (sin eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (sin eps))
5.0ms	(/ (* (tan x) (sin eps)) (cos eps))
17.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series611.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan x) (tan eps))
69.0ms	(* (tan x) (sin eps))
95.0ms	(/ (* (tan x) (sin eps)) (cos eps))
355.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	385	785
1	1424	711
2	5001	699

prune352.0ms

Filtered

82 candidates to 59 candidates (72.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	82	17	99

Merged error: 14.2b

Counts

99 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.7b	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
6×	`add-cube-cbrt` `times-frac`
5×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`frac-2neg` `clear-num` `associate-/r*` `frac-sub` `div-inv`
2×	`flip3--` `diff-log` `associate-*l/` `cos-mult` `flip--` `associate-/l/` `sin-mult` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3-+` `frac-add` `associate--l+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

13.0ms	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
23.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
93.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
94.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
538.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	546	2112
1	2412	1871
2	5001	1871

prune378.0ms

Filtered

102 candidates to 70 candidates (68.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	3	12	15
Picked	1	0	1
Done	0	1	1
Total	100	19	119

Merged error: 14.2b

Counts

119 → 19

regimes302.0ms

Accuracy

89.6% (0.8b remaining)

Error of 15.5b against oracle of 14.7b and baseline of 22.0b

bsearch128.0ms

Steps

Iters	Range		Point
10	6.435068213659741e-29	1.6162352712440818e-10	3.5816582224323186e-19
10	-3.4634588385797854e-17	-6.27478496522788e-29	-7.770309340641002e-24

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3272×	body	1280	valid
570.0ms	669×	body	2560	valid
368.0ms	1788×	body	640	valid
106.0ms	787×	body	320	valid
45.0ms	1121×	body	80	valid
35.0ms	363×	body	160	valid

Details

sample92.0ms

simplify4.0ms

prune4.0ms

localize8.0ms

rewrite11.0ms

series142.0ms

simplify77.0ms

prune123.0ms

localize11.0ms

rewrite34.0ms

series751.0ms

simplify44.0ms

prune412.0ms

localize16.0ms

rewrite33.0ms

series611.0ms

simplify42.0ms

prune352.0ms

localize22.0ms

rewrite54.0ms

series867.0ms

simplify63.0ms

prune378.0ms

regimes302.0ms

bsearch128.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling