Details

sample189.0ms

Algorithm

intervals

Results

89.0ms	119×	body	1280	valid
58.0ms	63×	body	640	valid
17.0ms	10×	body	2560	valid
6.0ms	22×	body	320	valid
6.0ms	29×	body	80	valid
3.0ms	13×	body	160	valid

simplify17.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
4.1b	(tan (+ x eps))

rewrite22.0ms

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:

15.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series144.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify976.0ms

Counts: 31 → 31

prune82.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
4.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite127.0ms

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:

9.0ms	(+ (tan x) (tan eps))
26.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(* (tan x) (tan eps))
75.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series745.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
209.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
91.0ms	(* (tan x) (tan eps))
355.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify470.0ms

Counts: 98 → 98

prune260.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
4.1b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

17×	`tan-quot`
16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-times` `associate-*r/` `frac-sub`
4×	`associate-*l/`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `flip--`

Counts

4 → 82

Calls

4 calls:

14.0ms	(* (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
21.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
905.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify646.0ms

Counts: 94 → 94

prune314.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
4.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

39.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
14.0ms	(/ (* (tan x) (sin eps)) (cos eps))
14.0ms	(* (tan x) (sin eps))
139.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series745.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
96.0ms	(/ (* (tan x) (sin eps)) (cos eps))
67.0ms	(* (tan x) (sin eps))
366.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify586.0ms

Counts: 120 → 120

prune316.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.9b

regimes180.0ms

Accuracy

86.3% (1.0b remaining)

Error of 15.5b against oracle of 14.5b and baseline of 21.8b

bsearch212.0ms

Steps

Iters	Range		Point
9	3.0715403066295787e-65	1.3361592146387383e-58	1.3189991825511699e-58
9	-4.88878821784254e-48	-1.867630740338721e-55	-9.631874247522397e-52

simplify536.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.0s	3432×	body	1280	valid
1.2s	594×	body	2560	valid
939.0ms	1745×	body	640	valid
556.0ms	780×	body	320	valid
231.0ms	1076×	body	80	valid
80.0ms	373×	body	160	valid